If x + y + z = 6 and x^2+y^2+z^2=20 then the value of x^3+y^3+z^3-3xyz is

RRB Junior Engineer Stage 1 Model Papers 10

Question : 3 of 98

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x + y + z = 6

and

x^2+y^2+z^2=20

then the value of

x^3+y^3+z^3-3xyz

Solution:

x + y + z = 6

On squaring,

x^2+y^2+z^2+2xy+2zy+2zx=36

⇒20+2(xy+yz+zx)=36

⇒xy+yz+zx=8

∴ x^3+y^3+z^3-3xyz

=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)

=6(20-8)=72

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